Walking on swinging slabs

Today, I was walking on a footpath made of cement slabs placed over a steel grid. I stepped over a cement block and I lost control before my autonomic nervous system saved me.

What happened was that the steel grid under one of the slabs was disfigured causing it to swing a little when anyone steps over it. Why and how does this swinging motion of the slab affect ones gait?

This can be understood by understanding how we walk. Put simply, we walk by taking steps and each step involves lifting the knee with the thigh muscles and giving the shinbone a forward velocity. This gives the step going forward some elevation as well as a forward velocity.

When we step on an accelerating platform like that swinging slab; as the slab is swinging downwards, the upward velocity the knee reaches with respect to the ground decreases. Hence, the foot does not reach the necessary elevation with respect to ground to make the next step.

There is a factor which leads to a decrease in the distance the knee can travel with respect to the surface it is standing too.

The force a leg can exert to lift the knee depends on the normal force the other leg can experience. In an accelerating platform like the swinging slab, the normal force that is exerted on the standing leg decreases because of psuedo forces acting upwards in the slab's frame of reference. When the normal force decreases, the force available for lifting the knee decreases. Hence, the height to which the knee can be lifted decreases with respect to the slab.

These two effects combine to create a situation where we cannot take a proper step after stepping on a swinging slab. The autonomic nervous system usually steps in in such situations to correct for the loss of height and velocity and corrects our course by causing an involuntary jerk.

Interested readers can calculate the amount of normal force lost when we step on a swinging slab by approximating it to be a cuboid and considering the force exerted by the foot to be a point force at a distance 'd' from the axis of the slab as follows: mg*d = I*alpha

where m is the mass of the person, g the gravitational constant, I is the moment of inertia of the slab and alpha the angular acceleration of the slab. From the value of alpha, the linear acceleration (a) of the foot located at a distance d from the axis can be calculated as 'a = d*alpha'. The decrease in normal force then becomes m*a.

Look out for my next post on rotating landscapes.